2(2w + w) = 36

February 22, 2026

Solving 2(2w + w) = 36: A Simple Step-by-Step Guide for Beginners

Understanding how to solve equations is a fundamental skill in algebra, and equation like 2(2w + w) = 36 is one of the most common beginners’ problems. In this article, we’ll walk you through solving this equation step-by-step, explain the key algebraic principles, and show how this method applies to real-world problem-solving.

What Does the Equation Mean?

The equation 2(2w + w) = 36 represents a real-life scenario where two times the sum of 2w and w equals 36. Breaking it down:

Inside the parentheses: 2w + w — combining like terms means w adds to 2w, giving 3w
Then multiplied by 2: 2 × 3w = 6w

So the equation simplifies to: 6w = 36

Step-by-Step Solution

Step 1: Simplify the expression inside the parentheses Start with the original equation: 2(2w + w) = 36

Since 2w + w = 3w, replace it: 2 × 3w = 36

Multiply: 6w = 36

Step 2: Isolate the variable w To solve for w, divide both sides of the equation by 6: 6w ÷ 6 = 36 ÷ 6

This gives: w = 6

Verifying the Solution

Plug w = 6 back into the original equation: 2(2×6 + 6) = 2(12 + 6) = 2×18 = 36 ✔️

The solution checks out!

Why Understanding This Matters

Solving 2(2w + w) = 36 isn’t just about finding w = 6—it’s about mastering essential algebraic tools:

Combining like terms: Combining 2w and w simplifies expressions for easier solving.
Distributing multiplication over addition: Applying the 2 to each term inside the parentheses correctly ensures accuracy.
Isolating variables: Dividing both sides to find the unknown variable is a core technique in any equation-solving scenario.

These skills apply to budgeting, physics, engineering, and everyday decision-making where proportional relationships matter.

Final Thoughts

Mastering simple equations like 2(2w + w) = 36 helps build confidence in algebra and strengthens logical thinking. Once you understand the mechanics, you’ll be prepared to tackle more complex expressions and real-world problems with clarity.

If you’re just starting, practice regularly using similar equations — soon, solving problems like this will feel second nature!

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By learning how to solve 2(2w + w) = 36, you’re not just solving one equation — you’re unlocking a key mathematical skill used in countless real-life applications. Keep practicing, and watch your confidence grow!